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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #32 : Simple Exponents

Convert to base .

Possible Answers:

2^8

2^4

2^3

2^6

2^2

Correct answer:

2^4

Explanation:

First, we know that is divisible by .

Therefore:

16=2^4

The answer is:

2^4

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Example Question #232 : Understanding Exponents

Convert $2^{15}$ to base .

Possible Answers:

8^9

8^5

$8^{12}$

8^6

8^4

Correct answer:

8^5

Explanation:

First, we know is divisible by .

Therefore:

8=2^3

We can set-up an equation by applying the power rule of exponents.

$2^{15}=(2^3)^x$

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

3x=15

Simplify.

x=5

The answer is:

8^5

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Example Question #233 : Understanding Exponents

Convert $3^{72}$ to base .

Possible Answers:

$9^{70}$

$9^{48}$

$9^{12}$

$9^{36}$

$9^{24}$

Correct answer:

$9^{36}$

Explanation:

First, know is divisible by .

Therefore:

9=3^2

We can set-up an equation by applying the power rule of exponents.

$3^{72}=(3^2)^x$

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

2x=72

Simplify.

x=36

The answer is:

$9^{36}$

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Example Question #701 : Mathematical Relationships And Basic Graphs

Convert 27^4 to base

Possible Answers:

$3^{12}$

$3^{9}$

$3^{15}$

$3^{18}$

$3^{7}$

Correct answer:

$3^{12}$

Explanation:

First, we know the following:

27=3^3

In order to figure out the whole exponent, we can apply the power rule for exponents.

$27^4=(3^3)^4=3^{12}$

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Example Question #702 : Mathematical Relationships And Basic Graphs

Evaluate:

$\frac{1}{5}^2$

Possible Answers:

$\frac{2}{25}$

$\frac{1}{25}$

$\frac{2}{5}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{25}$

Explanation:

We can expand $\frac{1}{5}^2$ to the following:

$\frac{1}{5}*\frac{1}{5}$

The product is:

$\frac{1}{25}$

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Example Question #236 : Understanding Exponents

Evaluate:

$\frac{3}{4}^3$

Possible Answers:

$\frac{9}{16}$

$\frac{27}{64}$

$\frac{27}{34}$

$\frac{9}{64}$

$\frac{27}{12}$

Correct answer:

$\frac{27}{64}$

Explanation:

We can expand $\frac{3}{4}^3$ to the following:

$\frac{3}{4}*\frac{3}{4}*\frac{3}{4}$

The product is:

$\frac{27}{64}$

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Example Question #237 : Understanding Exponents

Convert $\frac{1}{32}$ to base $\frac{1}{2}$

Possible Answers:

$\frac{1}{2}^{16}$

$\frac{1}{2}^7$

$\frac{1}{2}^{18}$

$\frac{1}{2}^5$

$\frac{1}{2}^4$

Correct answer:

$\frac{1}{2}^5$

Explanation:

First, we know that $\frac{1}{32}$ is divisible by $\frac{1}{2}$ .

The conversion becomes:

$\frac{1}{2}^5$

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Example Question #238 : Understanding Exponents

Convert $\frac{1}{125}$ to base $\frac{1}{5}$ .

Possible Answers:

$\frac{1}{5}^{25}$

$\frac{1}{5}^3$

$\frac{1}{5}^4$

$\frac{1}{5}^2$

$\frac{1}{5}^{10}$

Correct answer:

$\frac{1}{5}^3$

Explanation:

First, we know that $\frac{1}{125}$ is divisible by $\frac{1}{5}$ .

The conversion becomes:

$\frac{1}{5}^3$

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Example Question #231 : Exponents

Convert $\frac{1}{8}$ to base

Possible Answers:

$2^{\frac{1}{8}}$

$2^{-3}$

$2^{\frac{1}{3}}$

$-2^{3}$

2^2

Correct answer:

$2^{-3}$

Explanation:

We know that exponents raised to the negative power will generate fractions.

We also know that is divisible by .

8=2^3

However, since this a fraction, we then have the following:

$\frac{1}{8}=2^{-3}$ .

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Example Question #3372 : Algebra Ii

Convert 256 to base $\frac{1}{16}$

Possible Answers:

$\frac{1}{16}^{16}$

$\frac{1}{16}^{-2}$

$\frac{1}{16}^{\frac{1}{16}}$

$-\frac{1}{16}^{-2}$

$\frac{1}{16}^2$

Correct answer:

$\frac{1}{16}^{-2}$

Explanation:

If fractions are raised to a positive integer exponents, we know we will generate fractions; however, if a fraction is raised by a negative integer exponent, our answer will be whole number instead.

For example:

$\frac{1}{2}^{-2}=\frac{1}{\frac{1}{2^2}}=\frac{1}{\frac{1}{4}}=4$

The following rule has been used in this scenario:

$x^{-a}=\frac{1}{x^a}$

In this formula, is a positive exponent raising the base .

We know 256=16^2 .

Since we are dealing with a integer and converting to fractional base, we know we need to have a negative exponent.

The answer is:

$\frac{1}{16}^{-2}$

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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #32 : Simple Exponents

Example Question #232 : Understanding Exponents

Example Question #233 : Understanding Exponents

Example Question #701 : Mathematical Relationships And Basic Graphs

Example Question #702 : Mathematical Relationships And Basic Graphs

Example Question #236 : Understanding Exponents

Example Question #237 : Understanding Exponents

Example Question #238 : Understanding Exponents

Example Question #231 : Exponents

Example Question #3372 : Algebra Ii

All Algebra II Resources

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